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White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure, and develop option pricing in a fractional Black-Scholesmarket with a noise process driven by a sum of fractional brownian motions with various Hurst indices.
Abstract: We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Oksendal, Duncan, Pasik-Duncan, and others. As an application we develop option pricing in a fractional Black-Scholesmarket with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.

291 citations

Journal ArticleDOI
TL;DR: A fundamental asymptotic limit of sample-eigenvalue-based detection of weak or closely spaced high-dimensional signals from a limited sample size is highlighted; this motivates the heuristic definition of the effective number of identifiable signals which is equal to the number of ldquosignalrdquo eigenvalues of the population covariance matrix.
Abstract: The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a mathematically justifiable, computationally simple, sample-eigenvalue-based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a sample-eigenvalue-based scheme is the computational simplicity and the robustness to eigenvector modelling errors which can adversely impact the performance of estimators that exploit information in the sample eigenvectors. There is, however, a price we pay by discarding the information in the sample eigenvectors; we highlight a fundamental asymptotic limit of sample-eigenvalue-based detection of weak or closely spaced high-dimensional signals from a limited sample size. This motivates our heuristic definition of the effective number of identifiable signals which is equal to the number of ldquosignalrdquo eigenvalues of the population covariance matrix which exceed the noise variance by a factor strictly greater than . The fundamental asymptotic limit brings into sharp focus why, when there are too few samples available so that the effective number of signals is less than the actual number of signals, underestimation of the model order is unavoidable (in an asymptotic sense) when using any sample-eigenvalue-based detection scheme, including the one proposed herein. The analysis reveals why adding more sensors can only exacerbate the situation. Numerical simulations are used to demonstrate that the proposed estimator, like Wax and Kailath's MDL-based estimator, consistently estimates the true number of signals in the dimension fixed, large sample size limit and the effective number of identifiable signals, unlike Wax and Kailath's MDL-based estimator, in the large dimension, (relatively) large sample size limit.

291 citations

Journal ArticleDOI
TL;DR: The entanglement is maximized for intermediate values of the cavity damping rates and the intensity of the white noise field, vanishing both for small and for large values of these parameters and thus exhibiting a stochastic-resonancelike behavior.
Abstract: An atom that couples to two distinct leaky optical cavities is driven by an external optical white noise field. We describe how entanglement between the light fields sustained by two optical cavities arises in such a situation. The entanglement is maximized for intermediate values of the cavity damping rates and the intensity of the white noise field, vanishing both for small and for large values of these parameters and thus exhibiting a stochastic-resonancelike behavior. This example illustrates the possibility of generating entanglement by exclusively incoherent means and sheds new light on the constructive role noise may play in certain tasks of interest for quantum information processing.

290 citations

Journal ArticleDOI
26 Jun 1989
TL;DR: In this paper, the switching pattern can be randomized by modulating the triangle carrier in sinusoidal PWM (pulse-width modulation) with bandlimited white noise, which can be used to avoid the concentration of harmonic energy in distinct tones.
Abstract: Acoustic noise in an inverter-driven AC electric machine can be reduced by avoiding the concentration of harmonic energy in distinct tones. One method to spread out the harmonic spectrum without the use of programmed PWM (pulse-width modulation) is to cause the switching pattern to be random. It is proposed that the switching pattern can be randomized by modulating the triangle carrier in sinusoidal PWM (pulse-width modulation) with bandlimited white noise. All the advantages of sinusoidal PWM are preserved with this technique. These include real-time control, linear operation, good transient response, and a constant average switching frequency. By controlling the bandwidth and RMS value of the pink noise modulation, it is shown that the instantaneous variation in switching frequency as well as the bandwidth of the energy spectrum in the machine can be specified within predetermined limits. Experimental results show the absence of acoustic noise concentrated at specific tones which is present with conventional sinusoidal modulation. >

290 citations

Journal ArticleDOI
TL;DR: The online EM schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes.
Abstract: Sequential or online hidden Markov model (HMM) signal processing schemes are derived, and their performance is illustrated by simulation. The online algorithms are sequential expectation maximization (EM) schemes and are derived by using stochastic approximations to maximize the Kullback-Leibler information measure. The schemes can be implemented either as filters or fixed-lag or sawtooth-lag smoothers. They yield estimates of the HMM parameters including transition probabilities, Markov state levels, and noise variance. In contrast to the offline EM algorithm (Baum-Welch scheme), which uses the fixed-interval forward-backward scheme, the online schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes. Similar techniques are used to derive online schemes for extracting finite-state Markov chains imbedded in a mixture of white Gaussian noise (WGN) and deterministic signals of known functional form with unknown parameters. >

289 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537